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Questions tagged [quantum-chemistry]

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In what cases do isotopes cause non-negligible effects in chemicals

For example, CO2 (carbon dioxide), there could be Carbon8-Carbon22 isotopes, and I'm not sure for oxygen. Wondering at what point there is some sort of non-negligible effect, and what the effect(s) ...
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19 views

Band formation in diamond

Why is it that in the band diagram of diamond does the sp3 hybridised orbital split into two forming valence band and conduction band? I thought that these sp3 hybridised orbital forms 4n bonding and ...
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2answers
55 views

What is a nuclear wave packet?

What is the definition of a nuclear wave packet ? I often see the term used but i don't know how it is defined. It seems to be connected to the Born-Oppenheimer approximation. Is it defined there and ...
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21 views

Branch of Physics that Examines Atoms Relationships

Is there a specific branch of physics that can examine and calculate the strengths of atomic or molecular bonds and predict how they are going to break, putting into consideration the surrounding ...
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2answers
63 views

What's meaning of velocity of electron? [closed]

How do we define velocity of microscopic particles at small scales. As for macroscopic particle we can scale the distance travelled by object. But this is not the case with electron. Still, while ...
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2answers
63 views

What is the simplest possible Hamiltonian that yields an Antisymmetric Wavefunction?

I am using a Split-Operator Fourier Transform (SOFT) technique to solve the time-dependent electronic Schrödinger Equation (TDSE) for a Hydrogen molecule under the Born-Oppenheimer approximation. So I ...
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11 views

Proof that Restricted Open-shell Hartree–Fock can not take the canonical form

In Frank Jensen's Introduction to Computational Chemistry ($\mathrm{2^{nd}}$ edition), on page 99, it says: For an ROHF wave function, it is not possible to choose a unitary transformation that ...
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1answer
86 views

$sp^3$ Hybridization wavefunctions and probability density

I have plotted a hydrogen-like sp3-hybrid orbital probability density and it looks like this: I can plot 4 overlapping probability densities in a tetrahedral shape: So far it looks OK. But when I'm ...
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1answer
79 views

1D Infinite Square Well: Box Suddenly Increase in Size. Why the coefficients can be derived by inner producting the wave functions?

I have read the question 1D Infinite Square Well: Box Suddenly Increase in Size. How treat this?. There are two key equations in the selected answer. $$\int_0^{2L} dx \ \psi^*_m\left(x\right) \Psi\...
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2answers
49 views

Basis Functions for Hartree Fock, and Configuration Interaction

I'm about halfway through the book Szabo and Ostlund, and while I think I understand the rough idea of Hartree-Fock and configuration interaction, there is something I would like to clarify. For one, ...
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19 views

Program for calculating transition amplitudes

I calculated transition amplitudes with MBPT analytically and used Slater-Condon rules. Now I have a very long expression and I would like to solve my matrix elements. Does someone know a program for ...
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Operator for change of state?

I am trying to model a quantum system that has only three different classical states, so that the Hilbert space is simply $\mathbb C^3$, and let's call its standard basis $e_1,e_2,e_3$, with each of ...
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65 views

Direction of the permanent dipole moment of the NH$_3$ molecule

What is the direction of dipole moment in a molecule of $\rm NH_3$? Is from hydrogen to nitrogen? Also do we take into account the dipole moment of the lone pair with hydrogen? When we must take into ...
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1answer
55 views

How to propagate Heller's model of the Gaussian Wave Packet? [closed]

I'm working on an undergraduate research project on gaussian wave packets, but am a pretty big noob in terms of theoretical chemistry and the like. I'm having a lot of difficulty grasping this concept ...
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16 views

Bond Type in Orthophosphate

How can we find out the bond nature in LiBaPO4 by using charge transfer values obtained through DFT calculations?
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3answers
317 views

Would an $H_2O$ Molecule actually look like this 3D representation if we could see it?

I'm trying to get a much better grasp on atoms and molecules and I am a visual learner. I found the above image here. This intuitively makes sense to me because I can see how the electron orbitals ...
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2answers
41 views

Sign of exchange integral in quantum chemistry?

I have a question about exchange integral in quantum chemistry. Usually, we learn that the sign of exchange integral is positive, so a triplet state has lower energy than singlet state. Is it ...
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2answers
65 views

What is the energy of an atomic orbital?

When we refer to energy of an atomic orbital what is this energy ? is potential energy ? but if is potential energy then shouldn't be considered the whole potential energy of the atom ( potential ...
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1answer
186 views

Putting high symmetry points labels to a band structure plot [closed]

So far I've got this plot using Quantum Espresso. I want to put gamma, X, L, etc labels to the k-path. Quantum Espresso's ouput states the following: ...
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1answer
54 views

What are some molecular systems which have quantum states that are measurably incompatible?

What I'm looking for is a molecular system, which we can produce in a lab, that is, A discrete variable system (ie, a finite dimensional hilbert space) It has observables that are incompatible with ...
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1answer
39 views

Electronic configuration

In chemistry the lithium electronic configuration is $$1s^22s^1 \, .$$ Can we prove this using approximation method like perturbation theory that this the ground state and not for example $1s^22p^...
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How to determine symmetry of the system from the term symbol?

I'm studying term symbols. I can derive them mechanically from the electron configuration using the complete table of microstates. Let's consider a typical example - an atomic carbon with the ...
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26 views

In what cases (precisely) are Hund's rules valid?

I can't find on any good source (such as a textbook) a precise specification about the cases when Hund's rules (especially Hund's third rule) for an electronic configuration of atom are valid (the ...
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1answer
45 views

Planck blackbody radiation

I am reading a chapter about blackbody radiation in my physics textbook, and I encountered the following equation: $$d\rho(\nu, T)=\rho_\nu(T)d\nu=\frac{8\pi k_BT}{c^3}\nu^2d\nu$$ which is a classical ...
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1answer
46 views

Reference request for symmetry breaking Hartree-Fock

Stationary mean-field solutions break symmetries of the many-body Hamiltonian in favour of lowering the energy, e.g. translational or rotational symmetry, despite $[H,P]=0$, or $[H,L_z]=0$, ...
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1answer
107 views

What would measuring the position of an electron in an electronic superposition look like?

In view of the Copenhagen interpretation, the state: $$\Psi = \frac{1}{\sqrt{2}}|0⟩ + \frac{1}{\sqrt{2}}|1⟩$$ is interpreted as "when the system is measured, you have a 50% chance of finding the ...
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0answers
50 views

How do I proceed with the following coulomb integral?

I am trying to solve the $H_{2}^{+}$ ion problem using Fourier transform approach. The Hamiltonian that I am trying to solve is as follows, $$H=-\frac{\hbar^{2}}{2m_{e}}\nabla^{2}_{e}-\frac{e^{2}}{4\...
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1answer
53 views

How to explain about Raman spectroscopy?

What is the definition of Raman spectroscopy? How to explain in brief about antistoke line and Stoke line and Rayleigh?
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99 views

What is orthogonalization energy when two atoms overlap?

In this paper, I read that: When two atoms overlap, quantum mechanics dictates that they be orthogonal to each other. This drives up the energy and leads to so-called Pauli exclusion. The amount of ...
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0answers
39 views

Is there a mathematical singularity in the relativistic contraction of valence orbitals as a function of nuclear charge?

I'm looking at Figure 1 on p. 2 of Jansen, "Effects of relativistic motion of electrons on the chemistry of gold and platinum" (2005) (should be a free download). From the bottom curve, there is such ...
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37 views

Do relativistically-contracted electron states have the same energy and angular momentum values?

I've been reading that electron bound states are defined by four quantum numbers, $n$, $l$, $m_l$, and $m_s$, respectively the principal quantum number, the azimuthal quantum number, the magnetic ...
3
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1answer
157 views

How can I do quantum chemistry with QED?

So I am a theoretical and computational chemist by trade and my usual zone of operation in the domain of quantum mechanics is Hartree-Fock and Density Functional Theories. I was thinking if there ...
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1answer
110 views

How exact are the Kadanoff-Baym equations?

In a General nonequilibrium Quantum chemical System, the Kadanoff-Baym equations have the form: $(i \partial_t -h_2-\Sigma_{H,2})G_<(1,2) = \delta_C(1, 2) + \int d3 \Sigma (1,3)G_<(3,2)$ where ...
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Stability of saturated energy levels

In The Feynman Lectures on Physics, Vol. 3, Section 15-5, there's a discussion of the stability of various benzene ions. It turns out that the ions for which the all the energy levels up to a certain ...
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52 views

Is there a DFT program that gives spin-orbit coupling matrix elements between different spin states of one electron?

I want to calculate spin-orbit coupling matrix element (SOCME) between singlet state and triplet state. I could get SOCMEs from molpro CASSCF calculation. Is there any open source DFT package that can ...
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1answer
49 views

Can diffusion occur without thermal motion of molecules?

If I would ask: What are the Basic mechanisms of diffusion? I would get the answer: Because of thermal Brownian Motion. But are there other causes besides Brownian motion for Diffusion? Can ...
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1answer
27 views

Is the Hartree-Fock approximation getting better and better for higher atoms?

As the atomic number $Z$ increases, is the Hartree-Fock approximation getting better and better, or worse and worse?
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31 views

Does a Conical Intersection imply that the HOMO-LUMO gap in a molecule is very small?

I came across some notes in which the author swiftly made this comment, that if there's always a large gap between the HOMO and the LUMO along a chemical reaction ("large" can mean at least bigger ...
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130 views

many-body problems and why they are so hard

I am currently reading my first course in electronic structure theory and i have questions relating to the complexity of the many-body Schrödinger equation for quantum chemistry. More precisely about ...
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118 views

How can special relativity account for the electron orbital clouds of (stationary) heavy elements when electrons don't orbit in a classical way?

Einstein's famous mass-energy equivalence equation is still used for calculations, but still often considered less physically meaningful since the atoms that comprise a material don't actually gain ...
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41 views

Significance of ground state energy in quantum chemistry

I'm reading a paper that says "The fundamental goal in electronic-structure problems is to solve for the ground-state energy of many-body interacting fermionic Hamiltonians" (ref: https://arxiv.org/...
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1answer
96 views

Pi-bond angular momentum

I quantum chemistry literatute one can find a statement about projection of the angular momentum on internuclear axis: The angular momentum vector for rotation about the bond will lie along the ...
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1answer
171 views

Shape of Hydrogen atom in excited state with nonzeros angular momentum

Solution of Schrödinger's equation for an Hydrogen atom is well known: $$\Psi_{n,l,m} (r, \theta, \phi) = N e^{\frac{-r}{n r_1}} R_n^l (r) P_l^m(cos \theta) e^{im\phi} \,.$$ If we interested with ...
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1answer
94 views

Linear response correlation functions

I'm working my way through Methods of Molecular Quantum Mechanics by R. McWeeny and have run into a derivation I can't seem to figure out. So in chapter 12, he obtains an expression for the first ...
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1answer
453 views

Why is the distinction between Mott Insulators and Charge Transfer Insulators important?

Strongly-correlated metals often become insulators due to the repulsive Coulomb interaction, and the basic model here is the Mott-Hubbard Model: $$H=-t\sum(\hat{c}_{i,\sigma}^{\dagger}\hat{c}_{j,\...
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1answer
132 views

What are sigma and pi bonds in physics language?

Chemists often discuss sigma and pi bonds. To a physicist, it's not easy to figure out what these actually are, as discussions tend to be full of lots of chemistry jargon about "antibonding", "...
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1answer
101 views

Corrections from violation of P-symmetry for chemistry, biochemistry, life?

Imagine a mirror image of a biological cell: all molecules replaced with their symmetric versions (enantiomers). At least in theory, we should be able to synthesize it (Wikipedia), for example for ...
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1answer
130 views

Why are high electronegativity atoms found in the periodic table's upper right corner?

Looking at a graphical representation of electronegativity in the periodic table reveals a pattern that, noble gases aside, electrognetivity increases as you move toward the upper right hand corner of ...
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Why does my Hartree Fock/SCF code work for small molecules (water, methane etc) but goes crazy for slightly larger ones (Benzene, Butadiene etc)?

I made a Hartree Fock code, in the psi4 package, following the formulas given on this page: http://sirius.chem.vt.edu/wiki/doku.php?id=crawdad:programming:project3 When I use the same geometry they ...
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399 views

Hartree-Fock decoupling of Hubbard model

Hartree-Fock approximation requires wavefunctions be as separable as possible. I know the basic idea of Hartree-Fock but having some trouble in formalism of second quantization. I am trying to ...